Reduce to lowest terms: $- \dfrac{5}{7} \div - \dfrac{5}{6} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{5}{6}$ is $- \dfrac{6}{5}$ Therefore: $ - \dfrac{5}{7} \div - \dfrac{5}{6} = - \dfrac{5}{7} \times - \dfrac{6}{5} $ $ \phantom{- \dfrac{5}{7} \times - \dfrac{6}{5}} = \dfrac{-5 \times -6}{7 \times 5} $ $ \phantom{- \dfrac{5}{7} \times - \dfrac{6}{5}} = \dfrac{30}{35} $ The numerator and denominator have a common divisor of $5$, so we can simplify: $ \dfrac{30}{35} = \dfrac{30 \div 5}{35 \div 5} = \dfrac{6}{7} $